To respect copyright, here is the link to the full article. This material may not be copied or distributed electronically or in any other format without the written permission of NCTM. www.nctm.org/WorkArea/DownloadAsset.aspx?id=42962 But another reason I don`t want to teach these tips and rules is that they don`t last. They are working for now. They work for the types of problems that students are working on right now, but when they move on to other types of problems, the rules no longer work. The article I want to share with you today was published almost 6 years ago, but many of the things mentioned in this article are still used in classrooms today. I can honestly say that I would probably still be doing a lot if I hadn`t read this article – but once we know better, we`ll do better. From time to time, someone will say something like, “I just need them to know that if you add two numbers, you`ll get more numbers.” Then my heart stops beating for a while. While you`re at it, don`t forget to leave a review on iTunes.
I`d like to hear what you think about it and how we can make sure we`re offering you content you`ll really like. These are just a few of my favorite rules that work because they illustrate the caveats we should really place when using procedural tricks of the trade in math lessons. Karp, Bush and Dougherty identify 12 rules that apply in elementary school classes, 13 rules that apply to middle classes, and 13 rules that apply (or before!) Your expiring Rules articles allow for great conversations in your math department or professional learning community (PLC). Using a protocol to conduct a textual discussion on an article like this helps teachers develop their math knowledge for teaching while thinking about how to better serve their students. This table shows some commonly used languages that “expire” and more appropriate alternatives. How many of these “rules” did you say in class? Well, it turned out that an older child on the bus told him the rule: you just add a zero. My husband thought it was great that our 5 year old knew about it and was able to solve these problems. Until I explain how it doesn`t work because it will multiply by decimal numbers. And of course, he`s probably asking the same thing that many of you are asking, which is, “What should we do instead of saying you`re just adding a zero?” “1. If you multiply a number by ten, just add a zero to the end of the number.
This “rule” is often taught when students learn to multiply an integer by ten. However, this Directive shall not apply where the decimal places are multiplied (e.g. 0,25 × 10 = 2,5, not 0,250). Although this statement may reflect a regular pattern that students identify with integers, it is not generalizable to other types of numbers. Expiry date: Class 5 (5.NBT.2). “A rule that expires is something we tell our students that works now, but ends up not coming true. In each of their articles, they highlight a set of rules that teachers tell their students that at some point in their mathematical career, they are no longer true. They are very practical in the short term and usually have reservations that teachers omit, such as.” only for integers. What I like most about the Karp, Bush, and Dougherty articles is that they not only make these rules explicit, but also tell us when the rules expire, so we can consider alternatives. 13 rules, those of Karen S. Karp, Sarah B.
Bush and Barbara J. Dougherty changed my teaching forever. Not only do they share the 13 rules, but there is also a section on the expired mathematical language we use, and they give alternatives that can be used instead. This article is seriously a MUST-READ. To give you an overview of the article, I just want to share one of the rules with you today. Well, for those of you who are members of the Build Math Minds site, I have a video on how I can help kids understand what happens when you multiply (or divide) by a power of ten and how it all relates to help them understand the value of the place. I will buildmathminds.com/45 link on the “View Notes” page. Still on the View Notes page, I`m going to link to a video training I did on the rules that violate the rules that expire, as well as the link to article 13 Rules that expire so you can read the 13 rules. I was so guilty of telling this rule to the children. This made multiplying by 10 so easy.
In fact, it was so easy that my eldest son came home when he was in kindergarten and told me he could multiply by 10. He made some examples, and then I asked him how he knew. In the above scenario, I dig deep inside and question Dr. Karp`s strength. Luckily, she and her colleagues Sarah Bush and Barbara Dougherty gave us a lot of information with their series of “Rules That Expire” articles for classes K-5, 6-8 and high school. These articles appear in NCTM journals. Access to these archives justifies your membership in the NCTM. I found this article and it is worth sharing. It describes common rules and vocabulary that teachers share and that elementary school students tend to generalize – tips and tricks that don`t promote conceptual understanding, rules that “expire” later in students` mathematical careers, or vocabulary that isn`t accurate. Hey, have you already subscribed to the Build Math Minds podcast? If not, be sure to do it today because I don`t want you to miss episodes! Click here to subscribe to the podcast in iTunes. Why is this problematic? A great question! When these rules expire later, students are confused because their beloved teacher has told them that it has always been true. This confusion becomes confusion, and this confusion becomes an aversion to mathematics.
As Yoda once said, fear leads to anger. Anger leads to hatred. Hatred leads to suffering. Thirteen rules that expire: 1. If you multiply a number by ten, simply add a zero to the end of the number. 2. Use keywords to solve word problems. 3.
You can`t take a larger number from a smaller number. 4. Addition and multiplication make numbers larger. 5. Subtraction and division reduce numbers. 6. They always divide the largest number by the smallest number. 7.
Two negative points are a positive. 8. Multiply everything in parentheses by the number outside the parentheses. 9. Incorrect fractions should always be written as a mixed number. 10. The number you specify first when counting is always less than the number that comes next. It`s not a quick thing that happens to your students, but the quick answer is to teach them the value of space and how, if you multiply by ten, make the number ten times larger, thus moving the number to the next space value. I was guilty of giving my students advice or rules that I thought would help them get an answer faster because in the past I thought my job was to help my students get answers. Now I see my work as a teacher as helping students make sense, and many of these tips had no “meaning” behind them. It was really just rules to help my students get an answer. Over-generalization of generally accepted strategies, the use of imprecise vocabulary, and the use of tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstandings later in students` mathematical careers.
Karen Karp is one of my personal heroines in mathematics. So much so that as a camt board member, I took the liberty of taking a photo with her at CAMT 2016 in San Antonio while she was the opening speaker! Serious fanboy moment. To leave a review, go to iTunes and click “Ratings & Reviews” and “Write a Review.” I can`t wait to hear your thoughts on the podcast. Welcome to the recovering traditionalists in episode 45. Today, we look at 13 rules that expire. To learn more about this topic, visit:www.nctm.org/publications/blog/blog.aspx?id=42623 How to cause suffering in future math classes? Here are some examples. Many of us are to blame at some point in our teaching careers, but it`s not too late to stop the old habits! Interested in joining the Build Math Minds website? Click here for more details and to sign up for the waiting list: buildmathminds.com/bmm your email address will not be published. Mandatory fields are marked by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty with * 13 rules expiring.
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